What are the achievements of Logic?

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Re: What are the achievements of Logic?
Lacewing: If I had to summarize your personal philosophy, I would say it is the following: "I don't tolerate bullshit."
Re: What are the achievements of Logic?
Science Fan wrote: ↑Tue Feb 27, 2018 10:45 pm Lacewing: If I had to summarize your personal philosophy, I would say it is the following: "I don't tolerate bullshit."
My Grandma used to listen thoughtfully to an explanation, and then she'd furrow her brow and say, "Cut the crap!"
I would be honored to carry on the tradition.

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Re: What are the achievements of Logic?
Lacewing: Well, if you ever sneak across the border to run for president, you've got my vote.

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Re: What are the achievements of Logic?
Mathematics is a subset of symbolic logic. What a silly thing to question. Try reading Suzanne Langer's 'Introduction to Symbolic Logic' before making such statements.Dapplegrim wrote: ↑Mon Nov 27, 2017 12:31 pm What are the achievements of logic? It would seem to be hard to identify them.
In contrast mathematics has huge achievements to its name, especially its use in the domain of physics.
But logic, whether pure and abstract or its application to language, does not have many, if any, achievements to its name.
'Socrates is mortal' and 'It is raining'  two classical conclusions of logic, can hardly be claimed as achievements.
Its main claim would seem to be that it claims to be 'true'. But by what logic is that claim to truth justified? And also what is meant by 'true' when applied to logic? It would appear to be only a label to indicate internal selfconsistency.
Does philosophy need this form of logic? If so what for?
Does anyone have any suggestions?
Re: What are the achievements of Logic?
Did you miss the memo from Gödel?
Re: What are the achievements of Logic?
If we were done, you wouldn't have bother responding.Lacewing wrote: ↑Tue Feb 27, 2018 9:09 pmIt would simply help explain your weird communication.
That is kind of hypocritical for someone open to "creative potential" and life experiences to pass judgement?
Sure, in the context of what I want to invest my energy on at any given time.
So what you "want" defines what is true and not true to you?
Sure it can. So? Why do I need to invest any more in it until it does?
You already are hooked in the conversation.
Yes, it appears to me that all things change with time and/or circumstances.
In the moment, and depending on the circumstance, a change in thinking may not be logical.
Then you do not always change do you? And what is logical exactly, past what you want and don't want?
What is this problem you have with accepting multiple things as being true? Are you so jacked up to have a set of solid, unmovable, absolute answers  to such a degree that you can't even function or adapt or flow? Or do you just like to argue?
Are you so jacked up to have a set of changing answer  to such a degree that you can't even function let alone know who you are?How many "identities" have you been through at this point? Do you even know who you are, or do you just respond to whatever changes come along?
Yes, both true. I do try to embrace everything in the human experience, but some things (like your stupid questions) are uncomfortable to continually wade through over and over, droning on and on, seemingly without end. Still, look at the effort I've made!
In all truth, I am not really impressed by your efforts, you seem like you are trying to please me, or someone...whatever.... To be quite frank the whole "multiple" experience argument usually equates to "I have had multiple jobs and multiple lovers all of which came and go, I have no control, I don't even know who I am anymore because of all the experiences, so I just let life use me for what it wants".
Several threads ago, I argue a standard time and place for everything argument. You agreed, however that argument strictly observes a constant, that what we understand of certain phenomena have a time and place (which is absolute) and when taken out of that proper time and place they cease to exist.
Yeh, whatever. You clearly don't understand half of what I say... so I'm not real surprised by your conclusion.
I don't think I am the only one who does not understand what you have to say...you are just a secular version of Nick. The whole "beauty in everything" approach seems like a cop out to not step outside you comfort zone.
I did. Are we done here?
Re: What are the achievements of Logic?
The only point I am arguing, relative to logic is this:Lacewing wrote: ↑Tue Feb 27, 2018 9:21 pmAs usual, you don't follow... What I've gotten good at is accepting and understanding the insane ramblings of people like you, by evolving to be amazed and amused at the creative potential.Eodnhoj7 wrote: ↑Tue Feb 27, 2018 8:51 pmGood then maybe you could explain your philosophy to me then...considering you claim I don't understand it.Lacewing wrote: ↑Tue Feb 27, 2018 8:46 pm There are definitely some crazy things that are said on this forum. Sometimes it's unfathomable how people could come up with such things. The way I've evolved to accept and understand it is to be amazed and amused at the creative potential. Sometimes it's easier than other times... but the more you do it, the easier it gets... and I've gotten pretty good at it.
Now, I'm done explaining obvious things to you. My energy is better used elsewhere.
There are constants, and what we understand of the constants is merely change as a form of approximation of the constants. Change exists as approximation however it is not a complete nor total truth in itself.

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Re: What are the achievements of Logic?
Re: What are the achievements of Logic?
So you're ignorant and proud of it? I don't follow your logic or rhetorical style. The incompleteness theorem destroyed the logicist program in 1931.Dalek Prime wrote: ↑Sat Mar 03, 2018 5:57 am No. I just used it to wipe my butt. Tell Kurt to send it again.
Re: What are the achievements of Logic?
ps  Perhaps underneath that moronic response was a genuine curiosity about logicism.Dalek Prime wrote: ↑Sat Mar 03, 2018 5:57 am
No. I just used it to wipe my butt. Tell Kurt to send it again.
From Wikipedia:
Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.
...
Kurt Gödel's incompleteness theorem undermines logicism because it shows that no particular axiomatization of mathematics can decide all statements. Some believe that the basic spirit of logicism remains valid because that theorem is proved with logic just like other theorems. However, that conclusion fails to acknowledge any distinction between theorems of firstorder logic and those of higherorder logic. The former can be proven using the fundamental theorem of arithmetic (see Gödel numbering), while the latter must rely on humanprovided models. Tarski's undefinability theorem shows that Gödel numbering can be used to prove syntactical constructs, but not semantic assertions. Therefore, any claim that logicism remains a valid concept relies on the dubious notion that a system of proof based on manmade models is as authoritative as one based on the existence and properties of the natural numbers.
If you have any more questions as to why we now know that math is NOT reducible to logic, feel free to post about wiping your butt. It makes us all very impressed with your intelligence.
Re: What are the achievements of Logic?
wtf wrote: ↑Sat Mar 03, 2018 11:49 pmps  Perhaps underneath that moronic response was a genuine curiosity about logicism.Dalek Prime wrote: ↑Sat Mar 03, 2018 5:57 am
No. I just used it to wipe my butt. Tell Kurt to send it again.
From Wikipedia:
Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic.
...
Kurt Gödel's incompleteness theorem undermines logicism because it shows that no particular axiomatization of mathematics can decide all statements. Some believe that the basic spirit of logicism remains valid because that theorem is proved with logic just like other theorems. However, that conclusion fails to acknowledge any distinction between theorems of firstorder logic and those of higherorder logic. The former can be proven using the fundamental theorem of arithmetic (see Gödel numbering), while the latter must rely on humanprovided models. Tarski's undefinability theorem shows that Gödel numbering can be used to prove syntactical constructs, but not semantic assertions. Therefore, any claim that logicism remains a valid concept relies on the dubious notion that a system of proof based on manmade models is as authoritative as one based on the existence and properties of the natural numbers.
If you have any more questions as to why we now know that math is NOT reducible to logic, feel free to post about wiping your butt. It makes us all very impressed with your intelligence.
From a philosophical perspective, why is it necessary  or even desirable  for all statements of mathematics to be decidable?
What determines whether any particular statement (string of symbols) is mathematical or not?
If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely nonproblematic.
Re: What are the achievements of Logic?
When did I say undecidability is "problematic?"A_Seagull wrote: ↑Sun Mar 04, 2018 12:12 am If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely nonproblematic.
I simply pointed out the extremely well known fact that Gödel's 1931 incompleteness theorems destroyed the hopes of the logicists.
From that moment on, the claim that "math is reducible to logic" is simply false.
I gave the Wikipedia reference but anyone can consult SEP or any textbook on mathematical logic. This isn't a controversial issue, it's a standard fact.
Re: What are the achievements of Logic?
I wasn't trying to argue with you!wtf wrote: ↑Sun Mar 04, 2018 12:15 amWhen did I say undecidability is "problematic?"A_Seagull wrote: ↑Sun Mar 04, 2018 12:12 am If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely nonproblematic.
I simply pointed out the extremely well known fact that Gödel's 1931 incompleteness theorems destroyed the hopes of the logicists.
From that moment on, the claim that "math is reducible to logic" is simply false.
I gave the Wikipedia reference but anyone can consult SEP or any textbook on mathematical logic. This isn't a controversial issue, it's a standard fact.
I was just making inferences from Godel's conclusion.
Would you like to comment on my conclusion?
Re: What are the achievements of Logic?
Oh ok my misunderstanding.
Incompleteness/undecidability are fantastically problematic They lead to many philosophical questions. Like, what is truth? If reason can't lead to truth then the Western project is doomed. That's why the postmodernists are winning these days. The societal rejection of reason comes straight from math itself.
* From nonEuclidean geometry we know that math can't tell us what's true. It depends on your axioms.
* And Gödel told us that even when we choose a set of axioms, we still can't know what's true!
What is true? Rationality cannot tell us. Western civilization is at risk. Pick up a newspaper. Intersectionality is in; rationality is out.
Tell me, what do you think of my thesis? That nonEuclidean geometry and Gödel's incompleteness theorem are the root cause of the contemporary labelling of rationality itself as a tool of social oppression rather than one of human liberation?
Ok! You wrote:
It's terribly problematic. We can no longer rely on reason to know what's true. There's a straight line from Riemann and Gödel to the suppression of free speech by social justice warriors.A_Seagull wrote: ↑Sun Mar 04, 2018 2:19 am If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely nonproblematic.
The entire Western tradition is at stake. Euclid's project has failed.
And look here. I have a datapoint for you. It's from an altright website but there's no reason to believe the information is false. If you hate altright websites I'll stipulate to your objection and you can forget I mentioned it. But it's out there, it's apparently true, and it's pretty depressing if one is a rationalist.
Students enrolled in a Physics 101 course at Pomona College last semester were required to complete a "Decolonizing Physics" project by calling attention to issues like "implicit bias" and "microaggressions."
https://www.campusreform.org/?ID=10586
I say this is the result of the lost of faith in rationality due to nonEuclidean geometry and incompleteness.
Re: What are the achievements of Logic?
It would seem to come down to what one wants from philosophy and perhaps what one expects from philosophy. And if there are expectations, what are those expectations and are they justified and if so how are they justified.wtf wrote: ↑Sun Mar 04, 2018 4:05 amOh ok my misunderstanding.
Incompleteness/undecidability are fantastically problematic They lead to many philosophical questions. Like, what is truth? If reason can't lead to truth then the Western project is doomed. That's why the postmodernists are winning these days. The societal rejection of reason comes straight from math itself.
* From nonEuclidean geometry we know that math can't tell us what's true. It depends on your axioms.
* And Gödel told us that even when we choose a set of axioms, we still can't know what's true!
What is true? Rationality cannot tell us. Western civilization is at risk. Pick up a newspaper. Intersectionality is in; rationality is out.
Tell me, what do you think of my thesis? That nonEuclidean geometry and Gödel's incompleteness theorem are the root cause of the contemporary labelling of rationality itself as a tool of social oppression rather than one of human liberation?
Ok! You wrote:
It's terribly problematic. We can no longer rely on reason to know what's true. There's a straight line from Riemann and Gödel to the suppression of free speech by social justice warriors.A_Seagull wrote: ↑Sun Mar 04, 2018 2:19 am If you do away with the requirement for all statements of maths to be decidable, then you are left with the statements (strings of symbols) that are theorems of the system i.e. those statements that have been deduced from the axioms. And that would seem to be entirely nonproblematic.
The entire Western tradition is at stake. Euclid's project has failed.
And look here. I have a datapoint for you. It's from an altright website but there's no reason to believe the information is false. If you hate altright websites I'll stipulate to your objection and you can forget I mentioned it. But it's out there, it's apparently true, and it's pretty depressing if one is a rationalist.
Students enrolled in a Physics 101 course at Pomona College last semester were required to complete a "Decolonizing Physics" project by calling attention to issues like "implicit bias" and "microaggressions."
https://www.campusreform.org/?ID=10586
I say this is the result of the lost of faith in rationality due to nonEuclidean geometry and incompleteness.
For me, truth is a label and there needs to be a process by which ideas or statements are labelled as 'true'.
So for mathematics the theorems of the system, which are deduced from the axioms, can be labelled as 'true' albeit only within the system of mathematics.